%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:59:21 AM UTC 2026
% Result : Theorem 0.11s 0.37s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 20 ( 8 unt; 0 def)
% Number of atoms : 242 ( 0 equ)
% Maximal formula atoms : 66 ( 12 avg)
% Number of connectives : 397 ( 175 ~; 146 |; 76 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 57 ( 0 sgn 48 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(reflexivity,axiom,
! [X] : r1(X,X),
file('theBenchmark.p',reflexivity) ).
fof(main,conjecture,
~ ? [X] :
~ ( ~ ( p100(X)
& ~ p101(X)
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| p1(X)
| ~ r1(Y,X) ) )
& ( p1(Y)
| ! [X] :
( ~ p100(X)
| ~ p1(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| p2(X)
| ~ r1(Y,X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ ( p100(Y)
& ~ p101(Y) )
| ( ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& p2(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& ~ p2(X) )
| ~ r1(Y,X) ) ) ) )
| ~ r1(X,Y) ) )
| ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) ),
file('theBenchmark.p',main) ).
fof(main_neg,negated_conjecture,
~ ~ ? [X] :
~ ( ~ ( p100(X)
& ~ p101(X)
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X] :
( ~ p100(X)
| p1(X)
| ~ r1(Y,X) ) )
& ( p1(Y)
| ! [X] :
( ~ p100(X)
| ~ p1(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X] :
( ~ p101(X)
| p2(X)
| ~ r1(Y,X) ) )
& ( p2(Y)
| ! [X] :
( ~ p101(X)
| ~ p2(X)
| ~ r1(Y,X) ) ) ) )
& ( ~ ( p100(Y)
& ~ p101(Y) )
| ( ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& p2(X) )
| ~ r1(Y,X) )
& ~ ! [X] :
( ~ ( p101(X)
& ~ p102(X)
& ~ p2(X) )
| ~ r1(Y,X) ) ) ) )
| ~ r1(X,Y) ) )
| ~ ! [Y] :
( p2(Y)
| ~ r1(X,Y) ) ),
inference(assume_negation,[status(cth)],[main]) ).
fof(nnf_2,plain,
? [X] :
( p100(X)
& ~ p101(X)
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X6] :
( ~ p100(X6)
| p1(X6)
| ~ r1(Y,X6) ) )
& ( p1(Y)
| ! [X5] :
( ~ p100(X5)
| ~ p1(X5)
| ~ r1(Y,X5) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X4] :
( ~ p101(X4)
| p2(X4)
| ~ r1(Y,X4) ) )
& ( p2(Y)
| ! [X3] :
( ~ p101(X3)
| ~ p2(X3)
| ~ r1(Y,X3) ) ) ) )
& ( ~ p100(Y)
| p101(Y)
| ( ? [X2] :
( p101(X2)
& ~ p102(X2)
& p2(X2)
& r1(Y,X2) )
& ? [X1] :
( p101(X1)
& ~ p102(X1)
& ~ p2(X1)
& r1(Y,X1) ) ) ) )
| ~ r1(X,Y) )
& ! [X0] :
( p2(X0)
| ~ r1(X,X0) ) ),
inference(fof_nnf,[status(thm)],[main_neg]) ).
fof(sk_main_neg_sk,plain,
( p100(sK0)
& ~ p101(sK0)
& ! [Y] :
( ( ( ~ p101(Y)
| p100(Y) )
& ( ~ p102(Y)
| p101(Y) )
& ( ~ p100(Y)
| ( ( ~ p1(Y)
| ! [X6] :
( ~ p100(X6)
| p1(X6)
| ~ r1(Y,X6) ) )
& ( p1(Y)
| ! [X5] :
( ~ p100(X5)
| ~ p1(X5)
| ~ r1(Y,X5) ) ) ) )
& ( ~ p101(Y)
| ( ( ~ p2(Y)
| ! [X4] :
( ~ p101(X4)
| p2(X4)
| ~ r1(Y,X4) ) )
& ( p2(Y)
| ! [X3] :
( ~ p101(X3)
| ~ p2(X3)
| ~ r1(Y,X3) ) ) ) )
& ( ~ p100(Y)
| p101(Y)
| ( p101(sK2(Y))
& ~ p102(sK2(Y))
& p2(sK2(Y))
& r1(Y,sK2(Y))
& p101(sK1(Y))
& ~ p102(sK1(Y))
& ~ p2(sK1(Y))
& r1(Y,sK1(Y)) ) ) )
| ~ r1(sK0,Y) )
& ! [X0] :
( p2(X0)
| ~ r1(sK0,X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(X1,sK1(Y)),skolemize(X2,sK2(Y))],[nnf_2]) ).
fof(sk_main_neg,plain,
( p100(sK0)
& ~ p101(sK0)
& ! [VAR_0] :
( ~ p101(VAR_0)
| p100(VAR_0)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p102(VAR_0)
| p101(VAR_0)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ p100(VAR_0)
| ~ p1(VAR_0)
| ~ p100(VAR_1)
| p1(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ p100(VAR_0)
| p1(VAR_0)
| ~ p100(VAR_1)
| ~ p1(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ p101(VAR_0)
| ~ p2(VAR_0)
| ~ p101(VAR_1)
| p2(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0,VAR_1] :
( ~ p101(VAR_0)
| p2(VAR_0)
| ~ p101(VAR_1)
| ~ p2(VAR_1)
| ~ r1(VAR_0,VAR_1)
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| p101(sK2(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| ~ p102(sK2(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| p2(sK2(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| r1(VAR_0,sK2(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| p101(sK1(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| ~ p102(sK1(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| ~ p2(sK1(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( ~ p100(VAR_0)
| p101(VAR_0)
| r1(VAR_0,sK1(VAR_0))
| ~ r1(sK0,VAR_0) )
& ! [VAR_0] :
( p2(VAR_0)
| ~ r1(sK0,VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_main_neg_sk]) ).
cnf(c_3,negated_conjecture,
p100(sK0),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_4,negated_conjecture,
~ p101(sK0),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_14,negated_conjecture,
( ~ p100(A)
| p101(A)
| ~ p2(sK1(A))
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_15,negated_conjecture,
( ~ p100(A)
| p101(A)
| r1(A,sK1(A))
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_16,negated_conjecture,
( p2(A)
| ~ r1(sK0,A) ),
inference(split_conjunct,[status(thm)],[sk_main_neg]) ).
cnf(c_17,plain,
r1(A,A),
inference(clausify,[status(thm)],[reflexivity]) ).
cnf(c_28,negated_conjecture,
( ~ p100(sK0)
| p101(sK0)
| r1(sK0,sK1(sK0)) ),
inference(resolve,[status(thm)],[c_17,c_15]) ).
cnf(c_29,negated_conjecture,
( ~ p100(sK0)
| r1(sK0,sK1(sK0)) ),
inference(resolve,[status(thm)],[c_4,c_28]) ).
cnf(c_19,negated_conjecture,
r1(sK0,sK1(sK0)),
inference(resolve,[status(thm)],[c_3,c_29]) ).
cnf(c_30,negated_conjecture,
( ~ p100(sK0)
| p101(sK0)
| ~ p2(sK1(sK0)) ),
inference(resolve,[status(thm)],[c_17,c_14]) ).
cnf(c_31,negated_conjecture,
( ~ p100(sK0)
| ~ p2(sK1(sK0)) ),
inference(resolve,[status(thm)],[c_4,c_30]) ).
cnf(c_20,negated_conjecture,
~ p2(sK1(sK0)),
inference(resolve,[status(thm)],[c_3,c_31]) ).
cnf(c_32,negated_conjecture,
~ r1(sK0,sK1(sK0)),
inference(resolve,[status(thm)],[c_16,c_20]) ).
cnf(c_27,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_19,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL656+1.001 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n020.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 23:02:19 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.11/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.35 % Process 4025620 was started by sandbox2 on n020,
% 0.11/0.35 % Fri Sep 25 23:02:19 2026
% 0.11/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.36
% 0.11/0.36 % From the command line: assign(max_seconds, 300).
% 0.11/0.37
% 0.11/0.37 % SZS status Theorem for theBenchmark
% 0.11/0.37
% 0.11/0.37 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.11/0.37 % Length of proof is 11.
% 0.11/0.37 % Level of proof is 3.
% 0.11/0.37 % Maximum clause weight is 11.000.
% 0.11/0.37 % Given clauses 16.
% 0.11/0.37
% 0.11/0.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------